Autocorrelation of New Generalized Cyclotomic Sequences of Period pn

2010 ◽  
Vol E93-A (11) ◽  
pp. 2345-2348 ◽  
Author(s):  
Seok-Yong JIN ◽  
Young-Joon KIM ◽  
Hong-Yeop SONG
Keyword(s):  
Cyclotomic Sequences

scholarly journals Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yan Wang ◽  
Liantao Yan ◽  
Qing Tian ◽  
Liping Ding
Keyword(s):  
Autocorrelation Function ◽  
Linear Complexity ◽  
Minimal Polynomial ◽  
Binary Sequences ◽  
Cyclotomic Class ◽  
Cyclotomic Sequences ◽  
Autocorrelation Value

Ding constructed a new cyclotomic class V 0   , V 1 . Based on it, a construction of generalized cyclotomic binary sequences with period p q is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function C S w is 3-level if p ≡ 3 mod 4 , and C S w is 5-level if p ≡ 1 mod 4 . The linear complexity LC S > p q / 2 if p ≡ 1   mod   8 , p > q + 1 , or p ≡ 3 mod 4 or p ≡ − 3 mod 8 . The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity.

A new class of quaternary generalized cyclotomic sequences of order 2d and length 2pm with high linear complexity

2018 ◽  
Vol 16 (01) ◽  
pp. 1850006 ◽  
Author(s):  
Longfei Liu ◽  
Xiaoyuan Yang ◽  
Bin Wei ◽  
Liqiang Wu
Keyword(s):  
Finite Fields ◽  
Linear Complexity ◽  
Periodic Sequences ◽  
New Class ◽  
New Family ◽  
Generalized Cyclotomic Classes ◽  
Cyclotomic Sequences

Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudo-random properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. In this paper, we construct a new family of quaternary generalized cyclotomic sequences with order [Formula: see text] and length [Formula: see text], which generalize the sequences constructed by Ke et al. in 2012. In addition, we determine its linear complexity using cyclotomic theory. The conclusions reveal that these sequences have high linear complexity, which means they can resist linear attacks.

Divisibility Properties of Some Cyclotomic Sequences

1980 ◽  
Vol 87 (7) ◽  
pp. 561
Author(s):  
J. C. Lagarias ◽  
A. M. Odlyzko
Keyword(s):  
Divisibility Properties ◽  
Cyclotomic Sequences

scholarly journals Notes about symmetric m-adic complexity of generalized cyclotomic sequences of order two with period pq

2021 ◽  
Vol 2052 (1) ◽  
pp. 012007
Author(s):  
V A Edemskiy ◽  
S V Garbar
Keyword(s):  
Positive Integer ◽  
Ring Of Integers ◽  
Generalized Cyclotomic Classes ◽  
Cyclotomic Sequences

Abstract In this paper, we consider binary generalized cyclotomic sequences with period pq, where p and q are two distinct odd primes. These sequences derive from generalized cyclotomic classes of order two modulo pq. We investigate the generalized binary cyclotomic sequences as the sequences over the ring of integers modulo m for a positive integer m and study m-adic complexity of sequences. We show that they have high symmetric m-adic complexity. Our results generalize well-known statements about 2-adic complexity of these sequences.

scholarly journals 3-adic complexity of ternary generalized cyclotomic sequences with period

2021 ◽  
Vol 2052 (1) ◽  
pp. 012008
Author(s):  
V A Edemskiy ◽  
S A Koltsova
Keyword(s):  
Approximation Algorithm ◽  
Rational Approximation ◽  
Generalized Cyclotomic Classes ◽  
Definition Of ◽  
Cyclotomic Sequences

Abstract In this paper, we study the ternary generalized cyclotomic sequences with a period equal to a power of an odd prime. Ding-Helleseth’s generalized cyclotomic classes of order three are used for the definition of these sequences. We derive the symmetric 3-adic complexity of above mention sequences and obtain the estimate of symmetric 3-adic complexity of sequences. It is shown that 3-adic complexity of these sequences is large enough to resist the attack of the rational approximation algorithm for feedback with carry shift registers.

Autocorrelation values of quaternary cyclotomic sequence of length 2pm

2020 ◽  
Vol 18 (06) ◽  
pp. 2050047
Author(s):  
Huaning Liu ◽  
Xiaolin Chen
Keyword(s):  
Linear Complexity ◽  
Cyclotomic Sequences

We completely determine the autocorrelations of the quaternary cyclotomic sequences over [Formula: see text] of length [Formula: see text] presented in [P. Ke and S. Zhang, New classes of quaternary cyclotomic sequence of length [Formula: see text] with high linear complexity, Inf. Process. Lett. 112 (2012) 646–650] in general without the restrictions about [Formula: see text].

scholarly journals Autocorrelation Values of Generalized Cyclotomic Sequences with Period pn+1

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 950
Author(s):  
Xiaolin Chen ◽  
Huaning Liu
Keyword(s):  
Positive Integer ◽  
Linear Complexity ◽  
Character Sums ◽  
Binary Sequences ◽  
Square Sequences ◽  
Cyclotomic Sequences

Recently Edemskiy proposed a method for computing the linear complexity of generalized cyclotomic binary sequences of period p n + 1 , where p = d R + 1 is an odd prime, d , R are two non-negative integers, and n > 0 is a positive integer. In this paper we determine the exact values of autocorrelation of these sequences of period p n + 1 ( n ≥ 0 ) with special subsets. The method is based on certain identities involving character sums. Our results on the autocorrelation values include those of Legendre sequences, prime-square sequences, and prime cube sequences.

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